What is the solution for 9y^{''}+12y^'-5y=0 ?

The solution for 9y^{''}+12y^'-5y=0 is y=c_{1}e^{t/3}+c_{2}e^{-(5t)/3}

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9y^{''}+12y^'-5y=0

9 y^{^{''}} + 12 y^{^{'}} - 5 y = 0

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{5 t}{3}}

Solution steps

9 y^{''} (t) + 12 y^{'} (t) - 5 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{5 t}{3}}

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{5 t}{3}}

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What is the solution for 9y^{''}+12y^'-5y=0 ?
The solution for 9y^{''}+12y^'-5y=0 is y=c_{1}e^{t/3}+c_{2}e^{-(5t)/3}